Question
what is the positive solution to this equation?
4x^2+12x=135
4x^2+12x=135
Answers
Answered by
GPT 3.5
To find the positive solution to the equation 4x^2 + 12x = 135, we can rearrange the equation and then solve for x.
First, let's rewrite the equation in standard quadratic form:
4x^2 + 12x - 135 = 0
Now, we can solve the quadratic equation using various methods such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 4x^2 + 12x - 135 = 0, we have:
a = 4, b = 12, and c = -135
Plugging these values into the quadratic formula:
x = (-12 ± √(12^2 - 4*4*(-135))) / (2*4)
x = (-12 ± √(144 + 2160)) / 8
x = (-12 ± √(2304)) / 8
x = (-12 ± 48) / 8
This gives us two possible solutions:
x = (-12 + 48) / 8 = 36 / 8 = 4.5
x = (-12 - 48) / 8 = -60 / 8 = -7.5
Since we are looking for the positive solution, the positive solution to the equation 4x^2 + 12x = 135 is x = 4.5.
First, let's rewrite the equation in standard quadratic form:
4x^2 + 12x - 135 = 0
Now, we can solve the quadratic equation using various methods such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 4x^2 + 12x - 135 = 0, we have:
a = 4, b = 12, and c = -135
Plugging these values into the quadratic formula:
x = (-12 ± √(12^2 - 4*4*(-135))) / (2*4)
x = (-12 ± √(144 + 2160)) / 8
x = (-12 ± √(2304)) / 8
x = (-12 ± 48) / 8
This gives us two possible solutions:
x = (-12 + 48) / 8 = 36 / 8 = 4.5
x = (-12 - 48) / 8 = -60 / 8 = -7.5
Since we are looking for the positive solution, the positive solution to the equation 4x^2 + 12x = 135 is x = 4.5.